In this paper, primal and dual necessary/sufficient optimality conditions are investigated for vector optimization problem with set, cone and equality constraints. We establish some necessary optimality conditions for strict local Pareto minima in terms of contingent derivatives, contingent epiderivatives and contingent hypoderivatives with steady functions in Banach spaces to such problem. Under suitable assumptions, necessary optimality conditions become sufficient optimality conditions. Examples illustrate the applicability of the obtained results.

中文翻译：

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具有约束条件的向量优化问题中严格局部帕累托最小值的偶然表导数的最优条件

在本文中，研究了具有集合、锥和等式约束的向量优化问题的原始和对偶必要/充分最优条件。针对此类问题，我们根据在 Banach 空间中具有稳定函数的条件导数、条件表导数和条件次导数为严格局部帕累托最小值建立了一些必要的优化条件。在适当的假设下，必要的最优性条件变成了充分的最优性条件。实例说明了所得结果的适用性。